import time
from typing import Tuple, Dict, Union, List
import tensorflow as tf
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import numpy as np
from sklearn.manifold import TSNE
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_samples, silhouette_score
NUMBER_PARAM = 10
REGULARIZER_TYPE = 'kernel_regularizer'
LS_KERNEL_REGULARIZER = np.linspace(0, 1e-4, NUMBER_PARAM)
LS_ACTIVITY_REGULARIZER = np.zeros(NUMBER_PARAM)
(x_train, y_train), (x_test, y_test) = tf.keras.datasets.mnist.load_data()
x_train_norm = x_train/np.max(x_train)
x_test_norm = x_test/np.max(x_test)
The following model is to minimize loss function, $L_T$, in terms of loss from regular autoencoder, $L$, plus regularization term, $R$.
Encoding layer:
$h = \alpha_e(W_1 \times\ x + b_1)$, where $\alpha_e(.)$ is activation function ReLU,
and the number of hidden units in $h$ is 196. Hence $h$ is a 196x1 vector in 196-dim latent space, $W_1$ is 196x748 weight matrix and $b_1$ is the bias term in the form of 196x1 vector.
Decoding layer:
$x' = \alpha_d(W_2 \times\ h + b_2)$, where $\alpha_d(.)$ is activation function sigmoid, $x'$ is the output of the autoencoder
which is optimized to reconstruct back to input $x$.
Loss function:
$L_T = L + R = ||x - x'||^2 + \lambda_k\sum |W_1| + \lambda_k\sum |W_2|$, where $i$ is the number of hidden units, $\lambda_k\ $is kernel regularizer, l1 regularization is used.
class Autoencoder(tf.keras.Model):
def __init__(
self,
input_shape: Tuple[int,int],
encoding_dim: int,
activity_regularizer: float,
kernel_regularizer: float,
**kwargs
) -> None:
super().__init__(**kwargs)
self.encoding_dim = encoding_dim
self.encoder = tf.keras.Sequential([
tf.keras.layers.Flatten(),
tf.keras.layers.Dense(
encoding_dim,
activation='relu',
activity_regularizer=tf.keras.regularizers.L1(activity_regularizer),
kernel_regularizer=tf.keras.regularizers.L1(kernel_regularizer)
)
])
self.decoder = tf.keras.Sequential([
tf.keras.layers.Dense(
input_shape[0]*input_shape[1],
activation='sigmoid',
kernel_regularizer=tf.keras.regularizers.L1(kernel_regularizer)
),
tf.keras.layers.Reshape(input_shape)
])
def call(self, inputs):
encoded = self.encoder(inputs)
decoded = self.decoder(encoded)
return decoded
def training(
train_set: np.ndarray,
test_set: np.ndarray,
activity_regularizer: float,
kernel_regularizer: float,
encoding_dim: int,
) -> Dict[str, Union[Autoencoder, float, int, np.ndarray]]:
# build
autoencoder = Autoencoder(
input_shape=(28, 28),
encoding_dim=encoding_dim,
activity_regularizer=activity_regularizer,
kernel_regularizer=kernel_regularizer,
)
autoencoder.compile(optimizer='adam', loss='mse')
callback = tf.keras.callbacks.EarlyStopping(monitor='val_loss', patience=3, min_delta=0.0001)
# fit
print(f'Training start:')
print(f'activity_regularizer = {activity_regularizer}')
print(f'kernel_regularizer = {kernel_regularizer}')
start = time.time()
history = autoencoder.fit(
train_set, train_set,
callbacks=[callback],
epochs=100,
batch_size=256,
shuffle=True,
verbose=0,
validation_data=(test_set, test_set)
)
end = time.time()
# eval
training_loss = history.history.get('loss')[-1]
testing_loss = history.history.get('val_loss')[-1]
epoch = max(history.epoch)
print('Training results:')
print(f'training_loss = {training_loss}')
print(f'testing_loss = {testing_loss}')
print(f'epoch = {epoch}')
print(f'time passed = {int(round(end-start))}s')
print('-'*100)
# return
w1, _, _, _ = autoencoder.get_weights()
w1_reshape = w1.T.reshape((encoding_dim,28,28))
result = {
'hyperparam': {
'activity_regularizer': activity_regularizer,
'kernel_regularizer': kernel_regularizer,
},
'results': {
'training_loss': training_loss,
'testing_loss': testing_loss,
'epoch': epoch,
'model': autoencoder,
'w1_reshape': w1_reshape,
}
}
return result
training_results = list()
for kernel_regularizer, activity_regularizer in zip(LS_KERNEL_REGULARIZER,LS_ACTIVITY_REGULARIZER):
result = training(
train_set=x_train_norm,
test_set=x_test_norm,
activity_regularizer=activity_regularizer,
kernel_regularizer=kernel_regularizer,
encoding_dim=196
)
training_results.append(result)
Training start: activity_regularizer = 0.0 kernel_regularizer = 0.0 Training results: training_loss = 0.0015085224295035005 testing_loss = 0.0014974536607041955 epoch = 23 time passed = 33s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 1.1111111111111112e-05 Training results: training_loss = 0.020480716601014137 testing_loss = 0.020110029727220535 epoch = 51 time passed = 74s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 2.2222222222222223e-05 Training results: training_loss = 0.03193270042538643 testing_loss = 0.03145895153284073 epoch = 44 time passed = 76s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 3.3333333333333335e-05 Training results: training_loss = 0.044483479112386703 testing_loss = 0.04386400803923607 epoch = 41 time passed = 65s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 4.4444444444444447e-05 Training results: training_loss = 0.052824586629867554 testing_loss = 0.05212283879518509 epoch = 39 time passed = 62s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 5.555555555555556e-05 Training results: training_loss = 0.06020164489746094 testing_loss = 0.059739384800195694 epoch = 38 time passed = 60s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 6.666666666666667e-05 Training results: training_loss = 0.06459446251392365 testing_loss = 0.06418381631374359 epoch = 35 time passed = 63s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 7.777777777777778e-05 Training results: training_loss = 0.0652855709195137 testing_loss = 0.06483202427625656 epoch = 40 time passed = 67s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 8.888888888888889e-05 Training results: training_loss = 0.06881899386644363 testing_loss = 0.06871726363897324 epoch = 37 time passed = 58s ---------------------------------------------------------------------------------------------------- Training start: activity_regularizer = 0.0 kernel_regularizer = 0.0001 Training results: training_loss = 0.07010775804519653 testing_loss = 0.07004084438085556 epoch = 34 time passed = 46s ----------------------------------------------------------------------------------------------------
MSE loss ($L_T$) against hyperparameter, kernel_regularizer ($\lambda_k$), for training set and testing set
def loss_plot(results) -> None:
param = list()
training_loss = list()
testing_loss = list()
for result in results:
param.append(result['hyperparam'][REGULARIZER_TYPE])
training_loss.append(result['results']['training_loss'])
testing_loss.append(result['results']['testing_loss'])
plt.figure(figsize=(12, 8))
plt.plot(param, testing_loss, 'bs', label='testing_loss')
plt.plot(param, training_loss, 'r^', label='training_loss')
plt.ylabel('loss')
plt.xlabel(REGULARIZER_TYPE)
plt.title('Training loss vs testing loss')
plt.legend(loc='upper left')
plt.show()
plt.close()
loss_plot(results=training_results)
Sparsity of $h$ against hyperparameter, kernel_regularizer ($\lambda_k$), for training set and testing set
def _sparsity_map(x: int) -> None:
if x != 0:
return 1
else:
return 0
_sparsity_map_vec = np.vectorize(_sparsity_map)
def plot_sparsity(
results,
train_set,
test_set
) -> None:
param = list()
ls_training_sparsity = list()
ls_testing_sparsity = list()
for result in results:
param.append(result['hyperparam'][REGULARIZER_TYPE])
model = result['results']['model']
train_encoded_imgs = model.encoder(train_set).numpy()
test_encoded_imgs = model.encoder(test_set).numpy()
train_sparsity = np.sum(_sparsity_map_vec(train_encoded_imgs))/train_encoded_imgs.size
testing_sparsity = np.sum(_sparsity_map_vec(test_encoded_imgs))/test_encoded_imgs.size
ls_training_sparsity.append(train_sparsity)
ls_testing_sparsity.append(testing_sparsity)
plt.figure(figsize=(12, 8))
plt.plot(param, ls_testing_sparsity, 'bs', label='testing_sparsity')
plt.plot(param, ls_training_sparsity, 'r^', label='training_sparsity')
plt.ylabel('sparsity')
plt.xlabel(REGULARIZER_TYPE)
plt.title('Training sparsity vs testing sparsity')
plt.legend(loc='upper right')
plt.show()
plt.close()
plot_sparsity(
results=training_results,
train_set=x_train_norm,
test_set=x_test_norm,
)
Weight matrix of the encoder, $W_1$, is shown on a grey-scale heatmap. Each of the subplot showing a row frm $W_1$ reshaped to 28x28
def plot_w1(
w1: np.ndarray
) -> None:
w1_dim = int(np.sqrt(len(w1)))
fig, ax = plt.subplots(
nrows=w1_dim,
ncols=w1_dim,
figsize=(w1_dim,w1_dim)
)
plt.gray()
i = 0
for row in ax:
for col in row:
col.imshow(w1[i])
col.get_xaxis().set_visible(False)
col.get_yaxis().set_visible(False)
i = i + 1
plt.show()
plt.close()
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
plot_w1(
w1=result['results']['w1_reshape']
)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def plot_images(
img_gp: List[np.ndarray],
num_img: int,
) -> None:
_, ax = plt.subplots(nrows=len(img_gp), ncols=num_img, figsize=(num_img,len(img_gp)))
plt.gray()
for i, row in enumerate(ax):
tmp = img_gp[i]
for j, col in enumerate(row):
col.imshow(tmp[j])
col.get_xaxis().set_visible(False)
col.get_yaxis().set_visible(False)
plt.show()
plt.close()
num_img = 20
img = x_test_norm[:num_img]
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
model = result['results']['model']
encoded_img = model.encoder(img).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
decoded_img = model.decoder(encoded_img).numpy()
latent_dim = int(np.sqrt(len(encoded_img.T)))
encoded_img_reshape = encoded_img.reshape((num_img,latent_dim,latent_dim))
norm_encoded_img_reshape = norm_encoded_img.reshape((num_img,latent_dim,latent_dim))
img_gp = [img, encoded_img_reshape, norm_encoded_img_reshape, decoded_img]
plot_images(
img_gp=img_gp,
num_img=num_img,
)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def similarity_plot(
img: np.ndarray,
ls_label: List[int]
) -> None:
similarity_matrix = img @ img.T
ls_similarity = [list() for i in range(10)]
ls_disimilarity = [list() for i in range(10)]
for i, u in enumerate(similarity_matrix):
for j, v in enumerate(u):
if i == j:
continue
if ls_label[i] == ls_label[j]:
label = ls_label[i]
ls_similarity[label].append(v)
else:
label = ls_label[i]
ls_disimilarity[label].append(v)
plot_data = [
{
'data': ls_similarity,
'title': 'Cosine similarity of the latent vector with the same label'
},
{
'data': ls_disimilarity,
'title': 'Cosine similarity of the latent vector with the different label',
}
]
_, ax = plt.subplots(nrows=1, ncols=2, figsize=(24,8))
for idx, col in enumerate(ax):
col.boxplot(plot_data[idx]['data'])
col.set_title(plot_data[idx]['title'])
col.set_ylim([0,1])
col.set_xticks(range(1,11))
col.set_xticklabels(range(10))
col.set_xlabel('label')
col.set_ylabel('cosine similarity')
plt.show()
plt.close()
num_img = 1000
img = x_test_norm[:num_img]
img_label = y_test[:num_img]
for result in training_results:
hyperparam = result['hyperparam']
print(hyperparam)
model = result['results']['model']
encoded_img = model.encoder(img).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
similarity_plot(img=norm_encoded_img, ls_label=img_label)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
def tsne_plot(
space_gp: List[np.ndarray],
label: List[int]
) -> None:
_, ax = plt.subplots(nrows=1, ncols=2, figsize=(20,10))
for idx, col in enumerate(ax):
space = space_gp[idx]['space']
scatter = col.scatter(space[:,0], space[:,1], c=label, cmap='Spectral')
col.set_title(space_gp[idx]['title'])
col.set_xlabel('tsne 1')
col.set_ylabel('tsne 2')
col.legend(*scatter.legend_elements())
plt.show()
plt.close()
for result in training_results:
model = result['results']['model']
hyperparam = result['hyperparam']
print(hyperparam)
encoded_img = model.encoder(x_test_norm).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
print('fitting tsne for encoded_img')
tsne_space = TSNE(n_components=2, n_jobs=-1).fit_transform(encoded_img)
print('fitting tsne for norm_encoded_img')
tsne_space_norm = TSNE(n_components=2, n_jobs=-1).fit_transform(norm_encoded_img)
space_gp = [
{
'space': tsne_space,
'title': 'Latest space',
},
{
'space': tsne_space_norm,
'title': 'Normalized latest space',
},
]
tsne_plot(space_gp=space_gp, label=y_test)
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
fitting tsne for encoded_img
fitting tsne for norm_encoded_img
def kmean_plot(
img: np.ndarray,
max_n_cluster: int = 10,
) -> None:
_, ax = plt.subplots(nrows=2, ncols=5, figsize=(25,12))
ax = ax.flatten()
range_clusters = range(2,max_n_cluster+1)
for n_clusters in range_clusters:
kmeans = KMeans(n_clusters=n_clusters)
kmeans.fit(img)
labels = kmeans.labels_
avg_silhouette_score = silhouette_score(img, labels, metric='euclidean')
sample_silhouette_values = silhouette_samples(img, labels)
y_lower = 10
for i in range(n_clusters):
ith_cluster_silhouette_values = sample_silhouette_values[labels == i]
ith_cluster_silhouette_values.sort()
size_cluster_i = ith_cluster_silhouette_values.shape[0]
y_upper = y_lower + size_cluster_i
color = cm.nipy_spectral(float(i) / n_clusters)
ax[n_clusters-1].fill_betweenx(
np.arange(y_lower, y_upper),
0, ith_cluster_silhouette_values,
facecolor=color,
edgecolor=color,
alpha=0.7
)
ax[n_clusters-1].set_xlim([-0.1, 1])
ax[n_clusters-1].set_ylim([0, len(img) + (n_clusters + 1) * 10])
ax[n_clusters-1].text(-0.05, y_lower + 0.5 * size_cluster_i, str(i))
ax[n_clusters-1].set_xlabel('silhouette score')
ax[n_clusters-1].set_ylabel('cluster label')
ax[n_clusters-1].set_title(f'{n_clusters}-clusters')
ax[n_clusters-1].axvline(x=avg_silhouette_score, color="red", linestyle="--")
ax[n_clusters-1].set_xticks([-0.1, 0, 0.2, 0.4, 0.6, 0.8, 1])
ax[n_clusters-1].set_yticks([])
y_lower = y_upper + 10
plt.show()
plt.close()
ls_inertia = list()
for result in training_results:
model = result['results']['model']
hyperparam = result['hyperparam']
print(hyperparam)
encoded_img = model.encoder(x_test_norm).numpy()
norm_encoded_img = np.divide(encoded_img,np.linalg.norm(encoded_img, axis=1).reshape(-1,1))
space_gp = [
{
'space': encoded_img,
'title': 'Latest space',
},
{
'space': norm_encoded_img,
'title': 'Normalized latest space',
},
]
for space in space_gp:
print(f'img = {space["title"]}')
kmean_plot(img=space['space'])
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 1.1111111111111112e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 2.2222222222222223e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 3.3333333333333335e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 4.4444444444444447e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 5.555555555555556e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 6.666666666666667e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 7.777777777777778e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 8.888888888888889e-05}
img = Latest space
img = Normalized latest space
{'activity_regularizer': 0.0, 'kernel_regularizer': 0.0001}
img = Latest space
img = Normalized latest space